Question
A fair die is rolled 4 times. What is the probability that a 3 is obtained on at least one of the rolls? Round your answer to three decimal places.
Ask by Morgan Wells. in the United States
Mar 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability of rolling at least one 3 in 4 rolls is approximately 0.518.
Solution
Let
The probability of not obtaining a 3 on one roll is
When rolling the die 4 times, the probability that 3 is not obtained in any of the rolls is
Thus, the probability that a 3 is obtained on at least one roll is the complement:
Converting this to a decimal:
So, the probability that a 3 is obtained on at least one of the rolls is approximately
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Simplify this solution Beyond the Answer
To determine the probability of rolling a 3 at least once in four rolls of a fair die, it’s often easier to calculate the complementary probability: the probability of not rolling a 3 at all in those four rolls.
The probability of rolling a number other than 3 on a single roll of a fair die is
Now, the probability of rolling a 3 at least once is given by the complement of that probability:
Now, calculating that value:
Rounding to three decimal places, the probability of obtaining at least one 3 is
